Question

Sasha wrote the function f(x) = 10x - 65 to find the amount of money she would make after selling x t-shirts. Select all of the values below that are in the domain of Sasha's function.

Option 1: All real numbers
Option 2: x ≥ 0
Option 3: x ≤ 0
Option 4: x > 6.5

Answer 1

The correct domain for Sasha's function, f(x) = 10x - 65, is x ≥ 0, as Sasha can only sell zero or more t-shirts. Options including negative values or unnecessary restrictions do not accurately represent the domain.

Step-by-step explanation:

The domain of Sasha's function f(x) = 10x - 65, which represents the amount of money made from selling x t-shirts, can be determined by looking at the possible values of x.

• Option 1: All real numbers - This is not correct because selling a negative number of t-shirts is not possible in reality.
• Option 2: x ≥ 0 - This is correct because Sasha can sell zero or more t-shirts.
• Option 3: x ≤ 0 - This is not correct because it would include negative numbers, which don't make sense in this context.
• Option 4: x > 6.5 - While Sasha can sell more than 6.5 t-shirts, this restriction is unnecessary, and hence this option doesn't represent the full domain.

Therefore, the correct domain for Sasha's function is represented by Option 2: x ≥ 0.